Simple Interest
Math MCQs

Question :    If Sandra paid $4984 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4450

Solution & Explanation

Solution

Given,

Amount (A) = $4984

Rate of Simple Interest (R) = 3%

Time (T) = 4 years

Thus, Principal (P) = ?

Method (1) Using Formula

Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given

Formula to find the Principal (P)

Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)

⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]

⇒ A = P (1 + RT)

Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given

In the given question, we need to find the Principal (P)

Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get

$4984 = P (1 + 3% × 4)

⇒ $4984 = P (1 + ³/₁₀₀ × 4)

⇒ $4984 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $4984 = P (1 + ¹²/₁₀₀)

⇒ $4984 = P (^{100 + 12}/₁₀₀)

⇒ $4984 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4984

⇒ P = ⁴⁹⁸⁴/_¹¹²/100

⇒ P = 4984 × ¹⁰⁰/₁₁₂

⇒ P = ^{4984 × 100}/₁₁₂

⇒ P = ⁴⁹⁸⁴⁰⁰/₁₁₂

⇒ P = $4450

Thus, the sum borrowed (P) = $4450 Answer

Method (1) Using Unitary Method

Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given

Calculation of the Simple Interest

Let, the principal = 100

Here, since rate of simple interest = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

Calculation of the Amount

Since, in the question, time = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 3 = 12

Thus, simple interest for 4 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 4984, then the Principal = ¹⁰⁰/₁₁₂ × 4984

= ^{100 × 4984}/₁₁₂

= ⁴⁹⁸⁴⁰⁰/₁₁₂

= 4450

Thus, Principal = $4450

Thus, the sum borrowed = $4450 Answer

Similar Questions

(1) What amount does William have to pay after 5 years if he takes a loan of $3500 at 5% simple interest?

(2) If Paul paid $5640 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(3) How much loan did Karen borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7140 to clear it?

(4) How much loan did Jason borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8470 to clear it?

(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.

(6) If Susan paid $4380 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 6% simple interest?

(8) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?

(9) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.

(10) If Betty paid $4590 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.